Well, seeing as your teacher is the one making the tests, I’d trust her.

Active transport is the transport of molecules that requires energy, or ATP. This is most commonly used to move molecules from a lower concentration gradient to a higher concentration gradient (ie the movement of Na+ and K+ in a cell membrane), but active transport can exist anywhere, no matter the concentration gradient. Active transport is simply the only type of transport that causes molecules to deliberately go up a concentration gradient.

so I’d say both are right – active transport is most common in places with concentration gradients, but they can exist anywhere.

Active transport is when molecules move through protein pumps in the membrane using ATP energy generally against concentration gradient, however substances can still move from higher concentration to lower concentration region. The main reason we call it ACTIVE transport is because we need energy to move substances against concentration gradient but it doesn’t mean that it can’t happen the other way around.

yea active transport is moving against the concentration gradient, i.e. from a low to high concentration